Orthogonal space-like vectors.

Felpudio
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Hey, I read that if a four-vector is 'four-orthogonal' to a time-like four vector then it must be space-like. I showed this quite easily.

I also read that a space-like vector can be orthogonal to another space-like vector, but can't seem to prove it. I wondered if someone could help me.
 
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Take one vector pointing along the x-axis and the other pointing along the y-axis.
 
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